History Matching With Cumulative Production Data

Watson, Ted A.; Lane, Scott H.; Gatens, J.M.

doi:10.2118/17063-pa

Cited by 20 publications

(7 citation statements)

References 2 publications

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“…It follows that the covariance matrix for pressure-derivative errors must be directly related to the covariance matrix for pressure errors and the matrix that defines the linear transformation between pressure-derivative data and pressure data. In a related context, Watson et al 8 recognized that covariance had to be modified for history matching cumulative production data. In this work, we show how to construct the derivative data covariance matrix for use in nonlinear least-squares analysis.…”

Section: Mentioned Previously)mentioning

confidence: 99%

Nonlinear Regression: The Information Content of Pressure and Pressure-Derivative Data

Önür

Reynolds

2002

SPE Journal

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It is shown that commonly used procedures for estimating parameters by regressing on pressure-derivative data are based on incorrect covariance matrices and thus violate the underlying statistical basis for nonlinear least-squares parameter estimation. Although the resulting estimates of model parameters may be reasonable, calculated confidence intervals are meaningless. Here, we show how to compute the correct derivative data covariance matrix that should be used for estimating parameters by nonlinear least squares. It is also shown that the information content of derivative data cannot be greater than the information content of pressure data, in the sense that regression on derivative data with the proper covariance matrix does not yield smaller confidence intervals than those obtained by regressing on pressure data only. In fact, we prove that matching a data set, including all interior derivative data plus two appropriate pressure points, yields exactly the same estimates and confidence intervals that would be obtained by regressing on pressure data only. Nonlinear Parameter EstimationHere and throughout, p obs refers to the vector of measured or observed pressure data, and contains all N d pressure measurements

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Section: Mentioned Previously)mentioning

confidence: 99%

Nonlinear Regression: The Information Content of Pressure and Pressure-Derivative Data

Önür

Reynolds

2002

SPE Journal

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“…(13) with a specified distribution function P(r). The weighting matrix W is chosen on the basis of maximum likelihood principles [8]; in our work, we assume that the errors are mean zero and identically distributed, so that W is the identity.…”

Section: Development and Solution Of The Inverse Problemmentioning

confidence: 99%

Developing nuclear magnetic resonance imaging for engineering applications

Watson¹,

Hollenshead²,

Chang³

2001

Inverse Problems in Engineering

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Nuclear magnetic resonance (NMR) is a powerful, noninvasive measurement method which can be used to obtain spatially resolved information about fluid distributions within media. In the present work, an approach for quantitatively analyzing magnetic resonance imaging (MRI) data is extended for use with multiple spatial dimensions. A relaxation model is introduced and then used in an inverse problem to obtain local estimates of relaxation distributions. These distributions are then used to obtain spatial distributions of the intrinsic magnetization, the key quantity for quantification of NMR images. The inverse problem utilizes B-spline basis functions to represent the unknown relaxation distribution and a regularization term to stabilize the solution. The impact of the regularization is controlled through the use of a regularization parameter which is chosen using a data driven, computerized method based on nonparametric regression. The approach is demonstrated on laboratory data obtained from a Bentheimer sandstone sample to obtain one-and two-dimensional porosity distributions.

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“…through visual examination of a plot or statistical tests, of serial correlation of the residuals-the differences between observed and calculated data values at the conclusion of the history match. 17 On the basis of our error model for cumulative production. 17 (5) to be independent random variables.…”

Section: Case Studiesmentioning

confidence: 99%

“…17 On the basis of our error model for cumulative production. 17 (5) to be independent random variables. Fig.…”

Section: Case Studiesmentioning

confidence: 99%

An Analytical Model for History Matching Naturally Fractured Reservoir Production Data

Watson

Gatens²,

Lee

et al. 1990

SPE Reservoir Engineering

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This paper presents a method for analyzing production data from naturally fractured gas reservoirs. A normalized time is used to modify analytical solutions to model gas flow in finite, dual-porosity reservoirs. Procedures for validating the dual-porosity reservoir model, determining the suitability of simpler reservoir models, and determining the best parameter estimates are illustrated with field data from naturally fractured reservoirs.

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History Matching With Cumulative Production Data

Cited by 20 publications

References 2 publications

Nonlinear Regression: The Information Content of Pressure and Pressure-Derivative Data

Nonlinear Regression: The Information Content of Pressure and Pressure-Derivative Data

Developing nuclear magnetic resonance imaging for engineering applications

An Analytical Model for History Matching Naturally Fractured Reservoir Production Data

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